import { Field } from 'o1js';
import { FpU, FpA } from './fp.js';
declare const Fp2_base: (new (value: {
    c0: import("o1js").AlmostForeignField;
    c1: import("o1js").AlmostForeignField;
}) => {
    c0: import("o1js").AlmostForeignField;
    c1: import("o1js").AlmostForeignField;
}) & {
    _isStruct: true;
} & Omit<import("node_modules/o1js/dist/node/lib/provable/types/provable-intf.js").Provable<{
    c0: import("o1js").AlmostForeignField;
    c1: import("o1js").AlmostForeignField;
}, {
    c0: bigint;
    c1: bigint;
}>, "fromFields"> & {
    fromFields: (fields: import("node_modules/o1js/dist/node/lib/provable/field.js").Field[]) => {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    };
} & {
    fromValue: (value: {
        c0: bigint | import("o1js").AlmostForeignField;
        c1: bigint | import("o1js").AlmostForeignField;
    }) => {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    };
    toInput: (x: {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    }) => {
        fields?: Field[] | undefined;
        packed?: [Field, number][] | undefined;
    };
    toJSON: (x: {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    }) => {
        c0: string;
        c1: string;
    };
    fromJSON: (x: {
        c0: string;
        c1: string;
    }) => {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    };
    empty: () => {
        c0: import("o1js").AlmostForeignField;
        c1: import("o1js").AlmostForeignField;
    };
};
declare class Fp2 extends Fp2_base {
    static zero(): Fp2;
    static one(): Fp2;
    assert_equals(rhs: Fp2): void;
    canonical(): {
        c0: import("o1js").CanonicalForeignField;
        c1: import("o1js").CanonicalForeignField;
    };
    static fromUnreduced({ c0, c1 }: {
        c0: FpU;
        c1: FpU;
    }): Fp2;
    equals(rhs: Fp2): Field;
    neg(): Fp2;
    conjugate(): Fp2;
    add(rhs: Fp2): Fp2;
    add_fp(rhs: FpA): Fp2;
    sub(rhs: Fp2): Fp2;
    static sum(inputs: Fp2[], operators: (-1 | 1)[]): Fp2;
    mul_by_fp(rhs: FpA): Fp2;
    mul_by_non_residue(): Fp2;
    mul(rhs: Fp2): Fp2;
    square(): Fp2;
    inverse(): Fp2;
    static loadFromJson(json: any): Fp2;
}
export { Fp2 };